












[1] 1
[1] 1
[1] 0
[1] 0
Fitting the ARIMA models
Series: colgate
ARIMA(0,1,1)(1,0,0)[52]
Coefficients:
ma1 sar1
-0.7618 0.0312
s.e. 0.0450 0.0658
sigma^2 estimated as 0.002281: log likelihood=446.79
AIC=-887.59 AICc=-887.5 BIC=-876.74
Series: crest
ARIMA(0,1,1)
Coefficients:
ma1
-0.6641
s.e. 0.0431
sigma^2 estimated as 0.002082: log likelihood=458.98
AIC=-913.97 AICc=-913.92 BIC=-906.73
Ljung-Box test
data: Residuals from ARIMA(0,1,1)(1,0,0)[52]
Q* = 47.41, df = 53, p-value = 0.6907
Model df: 2. Total lags used: 55

Ljung-Box test
data: Residuals from ARIMA(0,1,1)
Q* = 40.09, df = 54, p-value = 0.9206
Model df: 1. Total lags used: 55



Series: colgate
Regression with ARIMA(0,1,1)(1,0,0)[52] errors
Coefficients:
ma1 sar1 TC43 AO102 LS136 TC196
-0.8593 0.0084 -0.1298 -0.1606 -0.0997 0.1412
s.e. 0.0323 0.0674 0.0345 0.0416 0.0223 0.0344
sigma^2 estimated as 0.001902: log likelihood=473.57
AIC=-933.15 AICc=-932.73 BIC=-907.83
Outliers:

Series: crest
Regression with ARIMA(0,1,1) errors
Coefficients:
ma1 LS136 AO167 TC196
-0.7885 0.1646 -0.1427 -0.1322
s.e. 0.0447 0.0263 0.0392 0.0343
sigma^2 estimated as 0.001747: log likelihood=484.43
AIC=-958.85 AICc=-958.63 BIC=-940.77
Outliers:

Length Class Mode
outliers 5 data.frame list
y 276 ts numeric
yadj 276 ts numeric
cval 1 -none- numeric
fit 19 forecast_ARIMA list
effects 276 ts numeric
times 3 -none- numeric
[1] 43 102 136 196
[1] 136 167 196
Series: colgate_outlier$yadj
ARIMA(0,1,1)
Coefficients:
ma1
-0.8598
s.e. 0.0312
sigma^2 estimated as 0.001867: log likelihood=473.57
AIC=-943.13 AICc=-943.09 BIC=-935.9
Series: crest_outlier$yadj
ARIMA(0,1,1)
Coefficients:
ma1
-0.7897
s.e. 0.0430
sigma^2 estimated as 0.001728: log likelihood=484.43
AIC=-964.86 AICc=-964.81 BIC=-957.62
Ljung-Box test
data: Residuals from ARIMA(0,1,1)
Q* = 44.403, df = 54, p-value = 0.8211
Model df: 1. Total lags used: 55

Ljung-Box test
data: Residuals from ARIMA(0,1,1)
Q* = 35.724, df = 54, p-value = 0.974
Model df: 1. Total lags used: 55



Intervention Model
possible convergence problem: optim gave code=1
Call:
arimax(x = crest, order = c(0, 1, 1), method = "ML", xtransf = data.frame(I1 = (1 *
(seq(crest) >= 136))), transfer = list(c(1, 0)))
Coefficients:
Se han producido NaNs
ma1 I1-AR1 I1-MA0
-0.7775 0.0401 0.1591
s.e. 0.0437 NaN NaN
sigma^2 estimated as 0.001896: log likelihood = 471.15, aic = -936.31
Training set error measures:
ME RMSE MAE MPE MAPE
Training set 0.00205205 0.04346805 0.03385271 -3.397657 16.76844
MASE ACF1
Training set 0.7955474 -0.01422081

Ljung-Box test
data: Residuals from ARIMA(0,1,1)
Q* = 45.428, df = 52, p-value = 0.7283
Model df: 3. Total lags used: 55


Call:
arimax(x = colgate, order = c(0, 1, 1), method = "ML", xtransf = data.frame(I1 = (1 *
(seq(colgate) >= 136))), transfer = list(c(1, 0)))
Coefficients:
ma1 I1-AR1 I1-MA0
-0.8091 0.0006 -0.1031
s.e. 0.0412 0.5132 0.0495
sigma^2 estimated as 0.002163: log likelihood = 453.02, aic = -900.04
Training set error measures:
ME RMSE MAE MPE MAPE
Training set -0.001964486 0.04641939 0.03643914 -2.941924 12.55462
MASE ACF1
Training set 0.7890364 0.05175557

Ljung-Box test
data: Residuals from ARIMA(0,1,1)
Q* = 39.99, df = 52, p-value = 0.888
Model df: 3. Total lags used: 55


Funcion TRansferencia
Call:
arimax(x = colgate, order = c(1, 0, 0), method = "ML", xtransf = data.frame(crest),
transfer = list(c(0, 20)))
Coefficients:
ar1 intercept crest-MA0 crest-MA1 crest-MA2 crest-MA3
0.2349 0.4049 -0.4667 -0.0304 -0.0253 0.0337
s.e. 0.0618 0.0079 0.0546 0.0547 0.0565 0.0581
crest-MA4 crest-MA5 crest-MA6 crest-MA7 crest-MA8
0.0715 -0.0238 0.0695 -0.0197 -0.0058
s.e. 0.0583 0.0589 0.0591 0.0592 0.0595
crest-MA9 crest-MA10 crest-MA11 crest-MA12 crest-MA13
-0.0081 -0.0163 0.0121 0.0005 0.0619
s.e. 0.0596 0.0596 0.0606 0.0605 0.0607
crest-MA14 crest-MA15 crest-MA16 crest-MA17 crest-MA18
0.0214 -0.0533 0.0200 0.0308 -0.0517
s.e. 0.0607 0.0605 0.0599 0.0594 0.0583
crest-MA19 crest-MA20
-0.090 0.0954
s.e. 0.057 0.0567
sigma^2 estimated as 0.00157: log likelihood = 463.15, aic = -880.31
Call:
arimax(x = colgate, order = c(1, 0, 0), method = "ML", xtransf = data.frame(crest),
transfer = list(c(0, 0)))
Coefficients:
ar1 intercept crest-MA0
0.2870 0.4198 -0.4203
s.e. 0.0582 0.0077 0.0268
sigma^2 estimated as 0.0018: log likelihood = 480.47, aic = -954.94
z test of coefficients:
Estimate Std. Error z value Pr(>|z|)
ar1 0.2870442 0.0581593 4.9355 7.995e-07 ***
intercept 0.4198273 0.0077222 54.3665 < 2.2e-16 ***
crest-MA0 -0.4202765 0.0268355 -15.6612 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Series: colgate
Regression with ARIMA(1,0,0) errors
Coefficients:
ar1 intercept xreg
0.2870 0.4198 -0.4204
s.e. 0.0581 0.0077 0.0268
sigma^2 estimated as 0.00182: log likelihood=480.47
AIC=-952.94 AICc=-952.79 BIC=-938.46

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